Help me find the most accurate rifle/caliber combination.

oneounceload suggests:
If you don't like the 6PPC, then look at the 6MMBR, built on the XP-100 action with a 16-18" barrel, medium stiffness - it will be light enough for coyote hunting yet can put all shots in one hole at 200 yards
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How big's the hole? Bullet diameter? 2 inches?

I've seen rifles put all their shots into one hole at 200 yards and the holes varied from bullet diameter to several inches. It depends on how many rounds are fired. 1 shot's guaranteed to make the hole bullet diameter.
 
Rifles vary between themselves due to machining accuracy, inletting, etc etc. The caliber doesn't really have that much to do with it.
 
Does $1500 include the scope price? Also, weight and accuracy are DIRECTLY related. The heavier the gun, the better the accuracy.

Snipers, accurate field shooters, carry a 13 - 15 rifle. Is that ok?

IMO, scope is the next most important factor. To keep from spending $1500 on the scope, I would look at the Super Sniper line. . . But the best for what you have written would be a Weaver 24x.

For rifles, I would look for a Savage in 6mm or 30 cal. Savage has some inherent design features which make it more accurate. Be careful of twist rate. Light, flat based bullets are usually most accurate in a slow for caliber twist like 1:12.

For an accurate caliber, I like 243 or 308. There are good flat based bullets available in each. Flat based bullets, light for caliber will give best 1,2,300 yd accuracy.

Once you eliminate benchrested fire, gun accuracy becomes so much less important to overall accuracy. Weight/balance, stock fit, trigger, scope match to target are the keys. All else is filler to a certain extent.
 
I'll bet that you can go to any major gun shop, pick any name brand rifle, (Winchester, Remington, Savage, etc, etc), off the rack, in any common caliber 223 - '06, and a good moderately prices scope and you'll find it will suit your purposes well with in your budget.

Cheeper ammo means more shooting, More shootign (assuming you apply the fundamentals) means a more accurate rifle.
 
Overall, rolling your own for ammo, the .223 is about as inexpensive as can be used.

The rifle? Many will do just fine. I gave $400 for a nearly-new Ruger 77 Mk II light sporter and put a $75 Timney trigger in it. I use an old Leupold Vari-X II 3x9x40 for which I paid $150. Weaver bases and rings; pretty cheap

This rifle has been half-MOA from the git-go. Ruinacious on prairie dogs to 300 yards with no problems in having a high percentage of hits. Misses are my fault, not the rifle's.
 
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